Analysis and Probability in Quantum Physics Pan - American Advanced Studies Institute

We consider the scattering amplitude associated to a Schröodinger operator with a short range potential at an energy which is a non-degenerate maximum of the potential. We prove an asymptotic expansion of the semi-classical scattering amplitude in this setting. We compute the phase as well as the leading order symbol in this asymptotic expansion. Our work is motivated by earlier asymptotic developments of the scattering amplitude by Vainberg, Guillemin, Yajima, Robert and Tamura, Michel, and Alexandrova. This is joint work with Jean Francois Bony and Thierry Ramond. James L. Borg University College Dublin/University of Malta E-mail: [email protected] Title: On some Scrödinger operators with random magnetic field Abstract: We present some results on the integrated density of states of Scrödinger operators with random vector potentials. We principally consider a model with a Poisson random distribution of smooth finite-width flux tubes. We study the density of states of the Pauli Hamiltonian for this model and obtain classical bounds for the Lifshitz tails. This is joint work with J.V. Pulé (Dublin). We present some results on the integrated density of states of Scrödinger operators with random vector potentials. We principally consider a model with a Poisson random distribution of smooth finite-width flux tubes. We study the density of states of the Pauli Hamiltonian for this model and obtain classical bounds for the Lifshitz tails. This is joint work with J.V. Pulé (Dublin). Chris Frayer University of Kentucky, USA E-mail: [email protected] Title: Scattering Theory for Singular Potentials Abstract: I will discuss some mathematics related to the direct scattering problem for singular potentials. In particular, we will discuss the Schrodinger operator −(∂x+a)(∂x−a). I will discuss some mathematics related to the direct scattering problem for singular potentials. In particular, we will discuss the Schrodinger operator −(∂x+a)(∂x−a).